The fast crash of the central temperature during sawteeth in tokamaks

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Abstract
A simple model of the crash phase of sawteeth in tokamaks is presented, which explains many of the significant experimental observations: small oscillations in the electron temperature prior to the crash (precursor), a short crash time, and large long‐lived oscillations in the electron temperature following the crash (successor). In tokamak discharges with good central confinement the temperature profile across the center of the discharge remains rather flat. In such profiles skin currents form that cause the safety factor q to fall below one at a finite radius rs while q(r=0)≂1. The sawtooth crash is caused by the m=n=1 tearing mode growing on such a profile. For a profile in which q falls below one by an amount Δq, the crash time is given by the helical Alfvén time τA/Δq, independent of the resisitivity. The size of the magnetic island of the precursor can be a small fraction of rs. In contrast, a remnant magnetic island of the order of rs survives the crash and causes the successor oscillation. Estimates of the decay time of the successor are given.